Decision based on lattice order preference structure

Decision making alternatives are sometimes incomparable with each other and violate the completeness axiom of the rational behavior axiom of von Neumann-Morgenstern. Lattice order theory has therefore been used to deal with the incomparability issue among alternatives. This paper proves that the incomparable relation of the set of alternatives in same level under lattice order structure is equal to equivalence relation. The alternatives set with lattice ordered structure is classified as subsets of alternatives in terms of their corresponding location layers. The subsets make up a chain structure under the preference relations of equivalence classes, which realizes the chain-forming of preference structure, and transforms the lattice order structure to total order or asymmetric weak order structure. A new decision making method based on lattice-ordered preference structure is proposed and the proposed method is efficient to make decisions for the incomparable paired alternatives in the decision making alternatives set.